Mathematical logic and foundations Definition

Predicate

Definition

Let $X$ be a set. A predicate on $X$ is a statement $P(x)$ with a variable $x$ that ranges over $X$ , such that $P(a)$ is a proposition for each $a \in X$ . More generally, a predicate $P(x_1, \dots, x_n)$ has $n$ variables, and $n$ is its arity.

Remarks

The predicate " $x > 3$ " on the integers gives the true proposition " $5 > 3$ " and the false proposition " $1 > 3$ ". A predicate on $X$ determines the set $\{x \in X \mid P(x)\}$ of the values that make it true. See set-builder notation. A predicate with two variables is a binary relation.

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Proposition concept
Predicate definition

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Tag	`0T3DPBG981`
URI	`m2://0T3DPBG981`
Kind	definition
Writing	W1 stated
MSC	03B10
Defines	Predicate
Uses	Proposition

Predicate

Definition

Remarks

Reading path

Where this leads

Further reading

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